"What happened at the U.S. Capitol yesterday was an insurrection against the United States, incited by the president. This president should not hold office one day longer," Schumer said in a statement Thursday.
Under the 25th Amendment, the president can be removed from duty if the vice president and majority of cabinet members determine he is unfit for office and unable to discharge the powers and his duties.
While the discussion is ongoing, CBS News reported that no formal presentation has been made to Vice President Mike Pence.
President-elect Joe's Biden, whose inauguration is less than two weeks away, blamed Trump for the siege.
"They weren't protesters. Don't dare call them protesters. They were a riotous mob, insurrectionists, domestic terrorists," Biden said. "[Trump] unleashed an all-out assault on our institutions of our democracy from the outset and yesterday was but the culmination of that unrelenting attack."
Schumer called on Pence to invoke the 25th Amendment.
"The quickest and most effective way -- it can be done today -- to remove this president from office would be for the Vice President to immediately invoke the 25th Amendment," his statement continued. "If the vice president and the cabinet refuse to stand up, Congress should reconvene to impeach the president."
"It's with a heavy heart I am calling for the sake of our Democracy that the 25th Amendment be invoked," Kinzinger wrote.
"If the 25th Amendment is not invoked today, Congress must reconvene immediately for impeachment and removal proceedings," Ocasio-Cortez tweeted.
"President Trump is a danger to our democracy and nation. He incited yesterday's chaos, violence, and destruction at the U.S. Capitol. His removal must be immediate and swift," Meng said in a statement. "Vice President Pence must invoke the 25 Amendment to protect our democracy from further strain. If this is not done, Congress must return to impeach and remove the President."
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House Speaker Nancy Pelosi threatened to impeach President Trump if the 25th Amendment is not invoked.
"I join the Senate Democratic leader in calling on the vice president to remove this president by immediately invoking the 25th Amendment. If the vice president and cabinet do not act, the Congress may be prepared to move forward with impeachment," Pelosi said.
Newly elected New York Rep. Mondaire Jones and 12 colleagues went on to introduce a resolution to impeach the president.
"Just this week, Donald Trump abused his power yet again, pressuring state officials to deny the results of the November election and inciting a violent mob to descend upon the legislative branch — all in an attempt to undermine the integrity of our democracy," Jones said in a statement. "We must ensure that this is Donald Trump's last opportunity to do harm."
"We have never seen a president of the United States attempt to overthrow the Congress, to cause harm to members of a Congress that represents all of us, to undermine and destroy our democratic system," de Blasio said. "That's what the president did. He called together a mob, he pointed them at the U.S. Congress, he told them go disrupt, destroy."
PHOTOS: Chaos At U.S. Capitol Building
Even longtime Trump loyalist William Barr, the former attorney general, issued a stunning statement.
"Orchestrating a mob to pressure Congress is inexcusable. The president's conduct yesterday was a betrayal of his office and supporters," Barr said.
CBS News has learned that members of Trump's cabinet are also discussing his potential removal.
In a video posted to Twitter on Thursday night, the president finally acknowledged that he will be leaving office, but he did not mention the fact that he lost or President-elect Biden.
"A new administration will be inaugurated on January 20th. My focus now turns to ensuring a smooth, orderly and seamless transition of power," Trump said.
Meanwhile, Education Secretary Betsy Devos has resigned, joining eight others, including Transportation Secretary Elaine Chao.
Dick Brennan contributed to this report.
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